Avoiding sharp accelerations can mitigate the impacts of a Ferry’s radiated noise on the St. Lawrence whales

Exposure to anthropogenic noise from the commercial fleet is one of the primary constituents of the acoustic pollution perturbing the environment of aquatic life. Merchant ships (e.g. bulkers, tankers) have been the focus of numerous studies for underwater noise source level determination and modeling. This work extends pre-existing studies to the ferry ship class. Hydrophone-based measurements of the N.M. Trans-Saint-Laurent ferry near the Rivière-du-Loup harbor (Rivière-du-Loup, QC CANADA) were obtained for 186 transits between 2020 July 22th and 2020 September 5th. For each transit, monopole source levels are estimated for two (2) different modes of operation i.e., the low-speed phases of acceleration/deceleration when the ferry launches/docks at Rivière-du-Loup and the passages at quasi-operational speed at the hydrophone’s closest-point-of-approach. Relative differences between the two (2) modes of operation are presented here in the low-frequency domain between 141 and 707 Hz. An average excess of 8 to 11.5 dB indicates that the ferry is likely one order of magnitude noisier, within this frequency band, during acceleration/deceleration when compared to passages at operational speed. This highlights that, in terms of marine mammal conservation, a significant reduction of the noise pollution could be achieved, for instance, by avoiding sudden speed changes in the vicinity of whales.

Automatic identification system. Ship positioning data from the Automatic Identification System (AIS) aboard the ferry was obtained from Parks Canada. The AIS system is an autonomous tracking system that provides GPS positions at frequent intervals as well as some information about the ship including speed and direction. AIS data are regularly used in conservation science 26 . The AIS data of the ferry was extracted during the study period and the timestamps were converted to local time.
For each AIS entry, the ferry's distance to the hydrophone (d) and its instantaneous speed-through-water (STW) were computed using respectively the ferry's position ( φ, ), and its course over ground (COG), speedover-ground (SOG) and the vector of surface currents orientation and speed from the closest prediction from hourly models at an approximate 250-m resolution (https:// ogsl. ca) 27,28 .

Methods
Bandwidth of interest. Details regarding the processing of the post-retrieval data are provided in "Appendix 1". Sound pressure levels (SPLs), hereafter referred to as the frequency-dependent received noise levels (RLs) at the hydrophone, were extracted using Matlab -supported PAMGuide 29 . RLs spectra were processed for a low-frequency bandwidth between f 0 = 141 Hz (see Eq. 3) and f 1 = 707 Hz (see details in "Appendix 1"). The lower and upper limits f 0 and f 1 are respectively attributed to the natural high-pass filter caused by the shallowdepth environment where measurements took place and signal contamination at mid-to-high frequencies (> 1 kHz).
Backpropagation and MSLs calculations. Details on the computation of source noise levels (SLs) are provided in "Appendix 2". The passive SONAR equation (see Eq. 6) is used to process SLs spectra between f 0 and f 1 by adding, frequency by frequency, RLs to the propagation loss sustained by the sound wave between the ferry and the hydrophone's position. Considering the shallow-depth and low-frequency domains characterizing this (1)  www.nature.com/scientificreports/ work, the parabolic-equation solver RAM 30 was used to predict sound attenuation along the lines-of-sight connecting the ferry to the hydrophone 31, with hydrometric (Observatoire global du Saint-Laurent) and geological 32 input data referenced therein. Integrated in the frequency domain between f 0 and f 1 , RLs and SLs spectra provide respectively broadband received levels BB RL  Generalized linear mixed model. A multi-parameter maximum likelihood approach via the minimization of the Akaike information criterion was used to assess the dependency between the ferry's MSLs and its  www.nature.com/scientificreports/ speed with emphasis on transits at CPA where recorded speeds in this work compare with the ferry's operational speed (see Table 1). Generalized linear mixed model (GLMM) analysis was conducted with the function lmer of the lme4 package 33 . The term "mixed" indicates that the model implies the use of at least one fixed effect (i.e., a variable for which we wish to quantify the effect on reported broadband source levels) and at least one random effect (in our case, the time of the day of the measurement). Confidence intervals and p-values (via Wald-statistics approximation) were calculated with the function sjt.lmer of the sjPlot package 34 .
Definitions. The following concepts are largely discussed in the next sections: • Acceleration phase: The 10-to-15 min time period required by the ferry to reach its operational speed following departure, at rest, from the Rivière-du-Loup dock.
• Deceleration phase: The 10-to-15 min time period used by the ferry to lower its speed from operational to full stop in its final approach at the Rivière-du-Loup dock.
These definitions also certainly apply to the Saint-Siméon dock although the required time periods for both phases can always vary depending on the sea state, crowding in the harbor, specific bathymetric features (e.g., ref. 35 ), and more.

Results
Ferry's MSL. Figure 2 displays results obtained from a typical case of an outgoing trip towards Saint-Siméon.
The ferry leaves Rivière-du-Loup at approximately 12:16 EDT, roughly 15 min late on its original schedule. Between 12:17 EDT and 12:31 EDT, the ship enters an acceleration phase towards its operational speed (see Table 1). The acceleration phase is always carried out in two (2) distinct steps as revealed by the double-peak signature of the acceleration profile, seen at 12:19 EDT and 12:25 EDT in the lower panel. This may suggest two (2) distinct modes of operation of the engines, the first to break the ship's inertia and the second to reach operational speed. By the time the ferry transits at CPA at 12:31 EDT, operational speed has been approximately reached and the acceleration declines towards 0 knot min −1 . The BB RL [ f 0 − f 1 ] profile shows that the highest noise levels recorded at the hydrophone coincide with the CPA position, where the source-to-hydrophone distance is minimal. Relatively high-amplitude features are also detected preceding CPA during the 14 min of the acceleration phase. Backpropagation of the RLs spectra indicates that the peak BB MSL [ f 0 − f 1 ] happened at 12:24 EDT when the ferry's STW was about 5 knots and climbing. Increase of the engines' regime during these moments of acceleration certainly contributes to the radiation of substantial underwater low-frequency noise on distances greater than 1 km. Figure 3 reveals similar trends for an incoming trip towards Rivière-du-Loup. Once the ferry has crossed CPA while traveling at quasi-operational speed at 11:08 EDT, a deceleration phase is initiated between 11:09 EDT and 11:19 EDT as it approaches the dock. An inverse double-peak signature characterizes the deceleration profile again pointing towards a change in the engines' regime during the ship's docking procedure. BB RL [ f 0 − f 1 ] measurements are highest at CPA but persisted with similar amplitude values well into the deceleration phase. Backpropagated BB MSL [ f 0 − f 1 ] suggested that the ferry is definitely noisier while decelerating towards its docking approach when compared to the radiated noise at near operational speed. This indicates that the ship's engines could be on a reverse-thrust mode rather than simply gliding in its docking approach.
Time periods of interest are identified here between the acceleration kickoff and the passage at CPA for outgoing trips, and the passage at CPA and the end of the deceleration downgrade for incoming trips. Table 5 displays the specific results for the CPA and acceleration/deceleration measurements. At CPA, local time ( t CPA ), ferry-to-hydrophone distance ( d CPA ), ferry's speed-through-water (STW CPA ) and acceleration ( a CPA ), and calculated broadband source levels (BB CPA MSL [ f 0 − f 1 ]) are provided. The local time of a given acceleration/deceleration event ( t acc ) was defined as the inflection point (i.e., change of sign of the jerk profile, d 3 r/dt 3 ) of the acceleration profile between the two (2) identified peaks (e.g., 12:22 EDT in Fig. 2d and 11:13 EDT in Fig. 3d). This favors the probability that source-level measurements, during the acceleration/deceleration phase, are gathered for the ferry operating in similar mechanical conditions from one transit to another. At t acc , Table 5 provides the ferry-to-hydrophone distance ( d acc ), ferry's speed-through-water (STW acc ) and acceleration ( a acc ) at jerk's sign change, and calculated broadband source levels (BB acc . Missing data in our AIS-based spreadsheet between 2020 August 11th and August 24th, and the fact that ferry was temporarily disabled for maintenance on 2020 August 30th prevent the use of these recordings in Table 5. Figure 4 shows how broadband source levels at t CPA and t acc behave with respect to the ferry's STW. For comparison, the Wittekind's 36 MSL models for merchant ships is also displayed. Figure 5 shows the comparison between median SLs spectra predicted at t CPA and t acc (see "Ferry's MSL" section) between f 0 and f 1 . At CPA, when the ferry usually travels at a quasi-operational speed (see Table 1), the agreement with the ferry model developed by 37  www.nature.com/scientificreports/ for typical days during the summer of 2020. The combined acceleration/deceleration phases account for roughly 20% the time required to complete a given trip. This suggests that the ship's source-level signature cannot be modeled using a constant operational speed approximation and that low-speed launching and docking events must be considered in the overall characterization of its acoustic impact. Given the results for the Kolmogorov-Smirnov statistics in Figs. 6 and 7 displays the BB ≡ BB acc

CPA versus acceleration/deceleration.
distributions for both outgoing and incoming trips treated separately. Assuming normal distributions, BB is centered on 8.04 ± 5.02(1σ ) dB for outgoing trips and 11.50 ± 4.67(1σ ) dB for incoming trips.

Effects of the Ferry's speed and acceleration on MSL.
Ferry-to-hydrophone distances ( d CPA , d acc ), speeds-through-water (STW CPA , STW acc ), and accelerations ( a CPA , a acc ) were treated as fixed effects in the GLMM statistics (see "Generalized linear mixed model" section). Results, shown in Table 3, suggest a correlation We verified that the fit of each of the four (4) models shown in Table 3 was good with the R package DHARMa version 0.4.5 38 . Table 5 shows broadband MSLs, frequency-integrated between 141 and 707 Hz, averaging at 171.28 ± 3.44(1σ ) dB and 182.72 ± 6.49(1σ ) dB respectively at t CPA for the CPA transits at quasi-operational speed and at t acc during the acceleration/deceleration phases close to the dock. Although uncertainties on the sediments' parameters www.nature.com/scientificreports/ (see "Appendix 2") raise concerns regarding comparisons with other studies, values obtained here for the noisy acceleration/deceleration mode are comparable with predictions of 36 , across the same frequency band, for merchant ships (see Fig. 4). This suggests that the low-frequency acoustical footprint of an accelerating ferry could be similar to the one of much larger tankers and bulkers traveling at operational speed (although a comparison between our MSLs results and results/predictions for other ships should be nuanced because of protocol's limitations; see "Discussion" section). Figures 4,5, and 6 reveal that the ferry radiates more noise during the low-speed acceleration/deceleration phases than during its design-speed operational mode. This is contrary to most SLs empirical models that usually propose a monotonically increasing trend of the radiated noise levels with traveling speed (e.g., [39][40][41] ). Since these models were almost all exclusively developed for quasi-operational speed transits, acceleration/deceleration has never been seen as a suitable predictor in MSLs modeling. Our results hence suggest that current MSLs models might underestimate the underwater noise radiated by ships during speed change phases, which could lead to non marginal errors for vessels that spend significant time in acceleration/deceleration modes such as ferries. This reinforces our assumption that conditions in whale habitats in the vicinity of busy harbors could be improved by limiting sharp accelerations/decelerations from vessels.

Discussion
In Fig. 7, the correlation with direction could be an indication of the ferry's anisotropic radiated sound field with higher noise levels being emitted at the stern close to the engines and propellers. This is geometrically plausible given azimuthal angles of view differing by cos −1 (d CPA /d acc ) (roughly 65 • ) between t CPA and t acc (see Table 5). Considering the time periods of interest defined in "Ferry's MSL" section, the stern of the ship faces the hydrophone only during the deceleration phase of incoming trips. This can also be seen in Fig. 6 where BB acc

MSL
[ f 0 − f 1 ] is slightly greater, on average 1.3 dB, for decelerated-incoming trips when compared to acceleratedoutgoing trips. Figure 6 also reveals a side-to-side asymmetry at CPA resulting in BB CPA MSL [ f 0 − f 1 ] being on average about 2 dB louder as seen from a port aspect (outgoing trips) when compared to starboard measurements (incoming trips). This agrees with the port/starboard noise directivity recorded for cargos (about 2-3 dB at f = 340-360 Hz) 42 and containers (< 9 dB for f < 50 Hz) 43 . www.nature.com/scientificreports/ Correlation between source-level measurements and corresponding STW values at CPA is suggested in Table 3 with slopes of 1.41 and 1.49 dB knot −1 , strongly agreeing with the 1 dB knot −1 value commonly reported in the literature for merchant ships [44][45][46] . These studies provide their results on typically much larger bandwidths than what was used in this work. Hence, it is reasonable to assume that the acoustical gain in dB per knot would exceed values reported here if the full bandwidth of the SLEB's audiogram (i.e., ∼ 150-150,000 Hz) would have been considered. The CPA configuration in this work is similar to what would have been used in the determination of MSLs empirical laws in the literature (e.g., 36,39,41,47 ). Hence, a correlation between source-levels and transiting speed is not surprising, although the relatively narrow distribution of the STW CPA values in Table 5 makes it difficult to properly assess the impact of speed on BB CPA MSL [ f 0 − f 1 ]. Accelerations at CPA are always close to 0 since, at this point, the ship always travels at relatively constant speed and, therefore, should have little impact on source-level measurements. We also found no direct correlation between a acc and broadband source levels BB acc MSL [ f 0 − f 1 ] retrieved from the acceleration/deceleration phases. As expected, source-level measurements are geometry independent and no correlation was found with the sourceto-hydrophone distances d, hence giving credence to the backpropagation algorithm in this range of frequencies (see "Appendix 2"). We suspect that a better correlation between source-level measurements and the ferry's engine's RPM 48 may have been found although RPM values could not be retrieved a posteriori for this study. Table 5 are summarized as follow.

Sources of uncertainties on values for BB
The 100-m mesh grid of the bathymetric data (see "Appendix 2") is the limiting factor in terms of spatial resolution. This could be of importance in the case of close ship-to-hydrophone interactions separated by a few hundreds meters (see d CPA in Table 5) if localized bathymetric irregularities of restrained dimensions are found along the line-of-sight connecting the source and the receiver.
The AIS data (see "Automatic identification system" section) requires our analysis to be carried out in averaged blocks of 1 min. For quasi-operational speed passages at CPA, we expect the ship's radiated noise to remain roughly constant. However, this can not be said for the acceleration/deceleration phase in which speed and likely engines' regime change quickly. High-amplitude spikes of change in the radiated noise levels could be lost in the averaging statistics.  Table 5. Gray and black data respectively correspond to measurements at t CPA and t acc . Broadband monopole source levels integrated between f 0 and f 1 as predicted by 36  www.nature.com/scientificreports/ The impacts of meteorological conditions were not considered. The wind's magnitude and orientation will have an impact on the release of energy required by the engines to maintain (or accelerate to) a given speed 48 . Sea conditions, that could add to the levels of noise received by the hydrophone, were also ignored (see Fig. 14 of 49 ). The geophysical parameters of the terrain sediments are also questioned given the dated low-resolution reference 32 used to quantify them in this work (see "Appendix 2").
The absence of ISO/ANSI standard measurements (for instance: shallow waters) limits our ability to isolate the contribution of environmental variables. Ainslie et al. 49 discussed the formal bases of a standard approach for the measurement of underwater radiated noise by vessels transiting in shallow waters (z < 30m). The authors in particular suggested the use of at least three (3) hydrophones deployed directly on the seabed in order to smooth out pseudo-noise effects caused by current flows. Figure 8 shows the synchronicity between the measured ambient noise and the tidal diurnal pattern in the neighboring quiet coastal island of Kamouraska. Quiet periods are correlated with the peaked low/high tides while currents engulf the hydrophone causing turbulent vortices and pseudo-noise during episodes of flood/ebb tides.
These limits would have been of concern if part of our objectives was to estimate absolute (as opposed to relative) MSLs values for the N. M. Trans-Saint-Laurent. However, this work mainly focuses on identifying mitigation avenues to reduce the ferry's acoustical footprint on a sensitive area frequented by the SLEB. All MSLs measurements are relative to the same ship transiting at the same location. Hence, it is reasonable to assume that uncertainties on MSLs values attributed to protocol's limitations do not impact the conclusions reached in this work.

Conclusion
A hydrophone deployment close ( 2 km) to the current route of the N. M. Trans-Saint-Laurent ferry allowed to estimate the ship's monopole source levels, frequency-integrated between 141 and 707 Hz, for different engines' regime. Phases of acceleration as the ferry launches from the nearby Rivière-du-Loup harbor, of deceleration as the ferry prepares to dock in the Rivière-du-Loup harbor, and of roughly constant quasi-operational speed as the ferry transits at the hydrophone's closest-point-of-approach were prioritized. This work is highlighted by the large numbers of transits (186) recorded for a single ship as opposed to other studies dedicated to ships' source-level characterisation that usually imply a much lower number of transits of the same ship or many transits but of different ships.
The main results of our study are:  Table 1). www.nature.com/scientificreports/ 1. A correlation of approximately 1.4 dB knot −1 was established between the ferry's speed-through-water in a quasi-operational mode at CPA and its monopole source levels. No other correlation could be determined between the computed monopole source levels and the ship's kinematical properties and sea conditions at the time of the recordings. This highlights the requirement of new standards for shallow water recordings in order to properly assess the role of environmental variables in the extraction of monopole source levels. 2. Results have shown that the ferry could be one order of magnitude ( 10 dB) noisier during sharp speed changes when compared to the constant design speed used at operational mode. Quick accelerations and decelerations likely impact the levels of low-frequency radiated noise on kilometers away from the source. This work provides an additional approach to mitigate underwater noise pollution by regulating, if possible, the engines' regime when ships and noise-sensitive marine mammals are in close encounters. 3. Anisotropy in the radiated noise field has been confirmed as a mean difference of 1.3 dB in monopole source levels was found in favor of stern-oriented recordings i.e., when engines and propellers faced the hydrophone. A port/starboard asymmetry of nearly 2 dB was also found as the ferry transited at CPA. 4. Given the lack of comparative studies in the literature, we cannot conclude if the results presented here are representative of the world's ferry fleet although it is not surprising that phases of acceleration/deceleration radiate more noise than transits at operational speed. To generalize this result, other ad hoc recordings of different ferries operating in ecologically sensitive habitats are required.
This work is, to our knowledge, the first to establish a causal relationship between a ship's acceleration and its underwater radiated noise. Two (2) mitigation avenues are proposed in order to restrain the acoustic disturbance of ferries in areas populated by noise-sensitive species: 1  Table 5. Percentiles are shown, from bottom to top, at 5% (dot), 10%, 25%, 50%, 75%, 90%, and 95% (dot). The central dot gives the mean of the distribution. Violin plots tracing out the shape of each distributions are added. The KS-statistic D between CPA and acceleration/deceleration measurements is fairly close to 1 for both outgoing and incoming trips, hence suggesting a genuine statistical difference in radiated source noise levels between both operational modes.    Table 5. Outgoing (in red) and incoming (in blue) ships are treated separately. Solid lines are the corresponding normal distributions fitted on each histogram.   www.nature.com/scientificreports/ speeds-through-water, and RPM will act as controlled parameters as the ferries' underwater radiated noise will be recorded during voluntary passages.

Appendix 1: Data processing following hydrophone retrieval
Local times are expressed with respect to the Eastern Daylight Time (EDT) zone (i.e., UTC-04:00). WAV files of the surrounding acoustic environment were recorded in continuous segments of 60 min, 12 times a day starting at the top of the hour, between 08:00:00 EDT and 19:59:59 EDT. Matlab -supported PAMGuide 29 was used to convert recorded WAV files into the frequency domain through power spectral density analysis by estimating the mean sound pressure levels (SPLs) in 1-second time windows from 1 to 144000 Hz. SPLs (in dB Hz −1 ) were extracted using the Welch method 50 with a Hann window 51 and a 50% overlap, and will be hereafter referred to as received noise levels (RLs) at the hydrophone's position. In order to match the temporal resolution of the AIS data, RLs spectra were averaged out into 1-min blocks providing 60 spectra for each 60-min WAV files, hence 720 spectra per day. The water column height at the hydrophone's position is regulated by the tidal height provided by the Fisheries and Oceans Canada's 2020 Tide Table for Rivière-du-Loup (https:// www. marees. gc. ca/ fr/ stati ons/ 3130). Time-dependent tidal heights, �h(t) , were linearly interpolated over the 12-h time period of continuous recordings throughout the 46 days of deployment. The water column height at the hydrophone's position is therefore defined as, where h 0 = 8 m (see "Acoustic data" section) and �h(t) is always positive.
According to Equation (1) Table 4). At frequencies approaching 1000 Hz, computed transmission losses (see "Appendix 2") often show a sudden increase that is not compensated by a substantial drop of the RLs obtained from the hydrophone's recordings. This translated into source levels profiles increasing from mid-frequencies and above, a feature that does not agree with the monotonically decreasing behavior typically predicted by source levels models (see, e.g., Fig. 4 of 36 , Fig. 9 of 52 , Fig. 11 of 53 ). This suggests that the noise signature detected above 1 kHz may not be attributed to the ferry itself but rather to a combination of non-laminar flow noise, instrumental self-noise and/or contamination of the fast-rotating engines of nearby pleasure crafts. Therefore, we used an upper cutoff frequency f 1 of 707 Hz which corresponds to the upper boundary frequency ( f high ) of the 1/3-octave band centered on 630 Hz (see Table 4).
(2) h(t) = h 0 + �h(t), www.nature.com/scientificreports/ Note that further testing for mid-to-high frequencies (1000-100,000 Hz) using the better adapted ray tracing approach 54 has confirmed that a very large proportion of the ferry's acoustic power is indeed found at frequencies below f 1 15 . Extending the frequency domain above f 1 has no statistical impact on the conclusions reached in this work.

Appendix 2: MSLs computation
All 60 of the averaged-out 1-min RLs spectra forming the 60-min time segments (see "Appendix 1") in which CPA occurrences between the ferry and the hydrophone happened were spectrally collapsed between f 0 and f 1 to obtain the broadband BB RL [ f 0 − f 1 ] measurement (in dB) for each minute of the corresponding hour. Hence, where i is the ith integer frequency between f 0 and f 1 . Equation (4) allows to track in time the impact of the transiting ferry on the noise budget of the hydrophone's surroundings.
Backpropagation, from the hydrophone's location to the ferry's position, was modeled using the split-step Padé approximation of the parabolic equation method 30 . The RAM algorithm was used to estimate the transmission loss (TL RAM ) due to the geometric sound attenuation sustained between the ferry (source) and the hydrophone's position (receiver). According to the mooring design (see "Acoustic data" section), at each moment, the receiver's depth, z r (t) , is provided by, where the height h(t) of the water column at the hydrophone's position is given by Equation (2). The source's depth, z s , was fixed at 2.94 meters according to ISO standard 11 , which represents 70% of the N.M. Trans Saint-Laurent draught of 4.2 m (see Table 1). Bathymetric data were retrieved from the Canadian Hydrographic Service and interpolated on a 100-m mesh grid. Sediment nature has been taken from the geological survey of 32 which reveals a mixture of clay, silt and sand in our zone of interest. Geo-acoustical properties of the seabed  www.nature.com/scientificreports/ were therefore approximated, according to Table 1.3 of 24 , to 1525 m s −1 , 1650 kg m −3 and 0.7 dB −1 p respectively for the compressional speed of sound ( c b,RdL ), density ( ρ b,RdL ), and compressional wave attenuation ( α p,RdL ) in the sediments. Uncertainties on the sediments' parameters along lines-of-sight connecting the ferry to the hydrophone may prevent from a direct comparison between the ferry's underwater radiated noise and the noise radiated by other ship classes of the SLE. However, relative comparisons of the ferry's radiated noise during different operational modes in the restrained area surrounding the hydrophone (d 1-2 km) are expected to hold.
Average water temperature and salinity profiles (with a 1-m resolution along the depth axis) are provided by the Observatoire global du Saint-Laurent close to our zone of interest (see Panels (a) and (b) of Fig. 9). In the figure's Panel (c), the corresponding speed of sound value at depth z, c w (z) , was provided by 55,]Equation2 . A highorder polynomial fit was then applied to the resulting c w (z) data and coefficients were stored and later used to construct RAM input files (e.g., see Fig. 2 of 56 ).
TL RAM was processed for each integer frequency between f 0 and f 1 . Transmission loss due to magnesium sulfate and boric acid contributions (TL abs ) was treated according to the theory developed by 57,58 with salinity and water acidity of 18‰ and 8 respectively. The water temperature at the time of the recording was provided by the output log file of the hydrophone for each 60-min block, ranging between 4.97 • C and 11.99 • C during the 46 days of data gathering. Frequency-dependent source-level (SLs) spectra were processed using the passive SONAR equation, where i is the ith frequency between f 0 and f 1 , TL RAM,i (φ, → φ 0 , 0 ) and TL abs,i (φ, → φ 0 , 0 ) are respectively the geometric and absorption sound attenuation sustained between the ferry's position ( φ, ) and the hydrophone's position ( φ 0 , 0 ), and RL i (φ 0 , 0 ) and SL i (φ, ) are respectively the sound levels measured at the hydrophone and the monopole source levels computed at the ferry's position.
BB MSL [ f 0 − f 1 ] (in dB) is the broadband value of the frequency-integrated SLs spectrum between f 0 and f 1 . Hence, which allows to track in time noise radiated from the ferry's position. Results at t CPA and t acc (see "Ferry's MSL" section) are shown in Table 5.Appendix 3: Signal-to-noise ratio Signal-plus-noise-to-noise level differences ( L ) at t CPA and t acc were computed for the 160, 200, 250, 315, 400, 500, and 630 Hz 1/3-octave bands (see Table 4) using the approach described in § 6.2 of 59 . In each case, the background profile was taken as the one spectrum with the lowest BB RL [ f 0 − f 1 ] value in all 60 spectra forming the corresponding 60-min block. Recorded at a local time close to those of the time periods of interest (see Table 5), this background spectrum is likely representative of the weather conditions, sea activity, pleasure-craft density (6) SL i (φ, ) = RL i (φ 0 , 0 ) + TL RAM,i (φ, → φ 0 , 0 ) + TL abs,i (φ, → φ 0 , 0 ),   www.nature.com/scientificreports/ and flow noise contamination prevailing during the ferry's transit. Whisker plots for L are shown in Fig. 10. Background noise adjustment on RLs measurements was hence judged unnecessary because of L values almost exclusively in excess of 10 dB (see Equation(4) of 59 ).

Figure 10.
Whisker plots of the signal-plus-noise-to-noise (SNN) level difference ( L ) for all 1/3-octave bands used in this work (see Table 4). (a) L distribution for signal recorded at t CPA (see Table 5). (b) L distribution for signal recorded at t acc (see Table 5). Percentiles are shown, from bottom to top, at 5% (dot), 10%, 25%, 50%, 75%, 90%, and 95% (dot). The central dot gives the mean of the distribution.